Thermalization with Chemical Potentials, and Higher Spin Black Holes
Ritam Sinha (Tata Institute of Fundamental Research, Mumbai)
We study the long time behaviour of local observables following a quantum quench in 1+1 dimensional conformal field theories possessing additional conserved charges besidesthe energy. We show that the expectation value of an arbitrary string of local observablessupported on a finite interval exponentially approaches an equilibrium value. The equilibriumis characterized by a temperature and chemical potentials defined in terms of the quenchedstate. For an infinite number of commuting conserved charges, the equilibrium ensemble isa generalized Gibbs ensemble (GGE). We compute the thermalization rate in a systematicperturbation in the chemical potentials, using a new technique to sum over an infinite numberof Feynman diagrams. The above technique also allows us to compute relaxation times forthermal Green’s functions in the presence of an arbitrary number of chemical potentials. Inthe context of a higher spin (hs[λ]) holography, the partition function of the final equilibriumGGE is known to agree with that of a higher spin black hole. The thermalization rate fromthe CFT computed in our paper agrees with the quasinormal frequency of a scalar field inthis black hole.